Much music at the time, 6th and 7th century, even in the west, was in Greek, which reigned for a while.
This was called Byzantine chant.
When Augustine brought chant to the west, he was imitating chant from the East.
Ambrosian chant, derived from Byzantine chant, was preserved in the south of Italy as Beneventan chant.
This gave way to Old Roman chant around the beginning of the 7th and 8th centuries.
The legend is that Old Roman chant was started by Gregory.
He codified it and so it was called Gregorian chant.
However, Old Roman chant is not Gregorian chant.
Gregorian chant comes only from the 9th and 10th centuries and onward.
It is not "Gregorian" at all but is Carolingian chant and comes from the Frankish kingdom and was resisted in Rome.
Old Roman was more Byzantine in sound. Gregorian was more plain.
Nathan O'Halloran, SJ